A reflexive Banach space whose algebra of operators is not a Grothendieck space

By a result of Johnson, the Banach space F=(⨁n=1∞ℓ1n)ℓ∞ contains a complemented copy of ℓ1. We identify F with a complemented subspace of the space of (bounded, linear) operators on the reflexive space (⨁n=1∞ℓ1n)ℓp (p∈(1,∞)), thus solving negatively the problem posed in the monograph of Diestel and...

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Bibliographic Details
Published in:	Journal of mathematical analysis and applications Vol. 401; no. 1; pp. 242 - 243
Main Author:	Kania, Tomasz
Format:	Journal Article
Language:	English
Published:	Elsevier Inc 01-05-2013
Subjects:	Banach space Grothendieck space Reflexive space Space of bounded operators Space of bounded operators Grothendieck space Banach space Reflexive space
Online Access:	Get full text
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Summary:	By a result of Johnson, the Banach space F=(⨁n=1∞ℓ1n)ℓ∞ contains a complemented copy of ℓ1. We identify F with a complemented subspace of the space of (bounded, linear) operators on the reflexive space (⨁n=1∞ℓ1n)ℓp (p∈(1,∞)), thus solving negatively the problem posed in the monograph of Diestel and Uhl which asks whether the space of operators on a reflexive Banach space is Grothendieck.
ISSN:	0022-247X 1096-0813
DOI:	10.1016/j.jmaa.2012.12.017